SMA LNDG VFR HAS NMAC WITH ANOTHER SMA ON SHORT FINAL APCH.

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I WAS APCHING LONG BEACH ARPT FROM FULLERTON AND HAD CONTACTED THE TWR. I WAS TOLD TO CONTACT THEM AGAIN AT 2000 FT OVER THE 605 FWY; WHICH I DID . THEY GAVE ME A STRAIGHT IN FOR RWY 25L WHICH I ENTERED ON A 45 DEG ANGLE. ANOTHER PLANE IN THE PATTERN WAS TOLD TO FOLLOW ME IN #4 POS FOR LNDG. HE HAD PRIOR BEEN IN #3 POS. WHILE MONITORING TWR I LISTENED TO THEM TELL THIS PLT I WAS AT HIS 11:00 POS AND 1000 FT. APPROX 1 MI FROM TOUCH DOWN I WAS TOLD TO MAKE AN IMMEDIATE R TURN AND TO GAR WHILE #4 PLANE WAS TOLD TO MAKE AN IMMEDIATE 360 DEG TURN TO THE L. #4 PLANE WAS SEQUENCED BACK IN FOR LNDG ON 25L WHILE I CROSSED OVER THE ARPT MIDCTR AND TURNED L TO ESTABLISH DOWNWIND. I THEN PROCEEDED THROUGH BASE AND FINAL AND ALSO LANDED. AS FAR AS I AM CONCERNED; PLT OF #4 PLANE WAS UNSURE OF HIS POS IN RELATION TO MINE AND MAY HAVE BEEN CONFUSED AS TO WHICH SMA HE WAS TO SEQUENCE BEHIND. I ALSO FEEL THE TWR SHOULD HAVE REPEATED THE INSTRUCTIONS WHEN #4 PLT DID NOT ACKNOWLEDGE SEEING ME. IT WAS HVY PATTERN TFC AND THESE THINGS HAPPEN.